Which of the following is a rational number between 5 and 514

Question

?(1 point)
Responses

525
5 Start Fraction 2 over 5 end fraction

517
5 Start Fraction 1 over 7 end fraction

26−−√
start root 26 end root

513

Answer 1

A rational number is a number that can be expressed as the quotient or fraction of two integers (i.e., in the form $\frac{p}{q}$ where $p$ and $q$ are integers and $q\ne 0$).

Let's evaluate the options given between 5 and 514:

1. 525: This is greater than 514.
2. $5\frac{2}{5}$: This can be expressed as $5+\frac{2}{5}=\frac{25}{5}+\frac{2}{5}=\frac{27}{5}=5.4$, which is between 5 and 514.
3. 517: This is greater than 514.
4. $5\frac{1}{7}$: This can be expressed as $5+\frac{1}{7}=\frac{35}{7}+\frac{1}{7}=\frac{36}{7}\approx 5.14$. This is also between 5 and 514.
5. $\sqrt{26}$: This is not a rational number (and it is approximately 5.1), but we need rational numbers specifically.
6. 513: This is less than 514 but greater than 5.

The rational numbers between 5 and 514 from these options are $5\frac{2}{5}$ and $5\frac{1}{7}$.

Thus, the correct responses that are rational numbers between 5 and 514 are:

• $5\frac{2}{5}$
• $5\frac{1}{7}$

If you are looking for just one answer, $5\frac{2}{5}$ is one valid option.